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Friday, 3 June 2011

Scattering

Rayleigh Scattering making sun sets

The Electromagnetic spectrum is a beautiful thing; every classroom needs one, it’s as important to scientists as the alphabet was to Shakespeare. The EM spectrum describes the range of frequencies (in cm-1 for the moccasin wearing Chemists) or wavelengths (in nm for us hip converse wearing physicists) that electromagnetic radiation can take. The most notorious of these is ‘light’ although ‘light’ isn’t one entity as such as it still hogs a large portion of wavelengths (380 to 780 nm); it’s like the Kevin Smith of aeroplanes. Using the whole spectrum has allowed us to see things both in artificial and natural luminance, make chips that allow us to play Angry Birds sat on the loo, and provide us with ways to make LASERs which surely is the best way to use and abuse EM radiation.

One thing I have always managed to get confused about during my 4 years studying Physics, apart from trying to remember the Taylor Expansion are all the different types of scattering that affect EM radiation.

So, firstly, a note about EM radiation – it’s not just a squiggle that seeps out from sources like the sun but actually composed of quanta called photons. This is the major difference between the classical and quantum model and leads onto wave-particle duality.

Scattering involves light ‘waves’ essentially bouncing off ‘particles’ or volumes of stuff but in the quantum world this is described as the interaction of the photons with the matter it encounters. It is responsible for a lot of attractive things for example the sheen or lustre of objects is caused by scattering so you can thank physics for the rise of bling culture. Although the colour of objects is mostly down to absorption, the colour of the sky is actually due to Rayleigh scattering.

We can categorise scattering into 2 distinct boxes; elastic and inelastic. Elastic scattering causes negliable energy transfer whereas inelastic scattering causes shifts in energy so that the radiation leaving the interaction has a different wavelength/frequency.

Here’s a handy table about elastic and inelastic scattering:

Under the category of elastic scattering:

Rayleigh scattering – This occurs when light meets a small spherical particle with arefractive index. The limit for Rayleigh scattering to occur is that the particle size is smaller than the wavelength of thelight.

Mie scattering – Similar to Rayleigh scattering except the particlesize is around the same size as the wavelength.

Geometric scattering – Size of the particle islarger than wavelength.

These 3 types of scattering constitute atmospheric scattering and you can model the propagation of radiation through any type of weather/environment using a combination of these 3 scattering regimes. It this no small feat, and involves lots of equations and something called MODTRAN. This was my life for 5 months, having to simulate the propagation of a laser through Maine. Doesn’t do so well in rain.

Stimulated Brillouin and Raman scattering is often used for amplification in fibres by choosing a lower frequency signal photon to inelastically scatter off a higher frequency pump photon to produce another low frequency signal photon. The aim is to always ‘reproduce’ something, in this case using the effects of scattering to reproduce a low frequency photon. It may sound boring but it is this process which allows us to have the broadband speeds we have, and research continues to find new ways to use processes like this to develop more amplification techniques.

Thomson scattering – this is the lil bro of Compton scattering (which is an inelastic process), he’s like totally on the lowdown, like..the low energy limit, that’s LOW. Anyway, it happens when EM radiation meets a free charged particle – like an electron. The E and B (electricand magnetic or as I’m now calling them, the ‘Bert and Ernie’) parts of the radiation cause a Lorentz force onto the charged particle causing it to accelerate. It then emits radiation at the same frequency as the perturbing radiation, hence conserving energy. The Lorentz force is a complex way of saying that a bit of the energy of the perturbing radiation gets transferred to the particle, causing it to move, so the particle emits radiation to stop moving. Thomson scattering is a main reason behind the linear polarization of the cosmic microwave background.

Inelastic Scattering

Since I’ve given a shout-out to Compton scattering already – this just involves the X ray and gamma ray part of the spectrum interacting with matter. The X/gamma-ray photon imparts energy to the matter atoms causing ionisation (excites the electrons in the atoms causing them to ping off like little fleas) therefore the photons decrease in energy after the interaction. This was one of the fundamental experiments to show wave-particle duality because in order for an electron to leave a quantised amount of energy must be transferred to it. Previously light was thought of as a wave, with an energy flux equal to the intensity (i.e. more light). So surely the higher the intensity the more electrons will ping off the metal surface? Well no. The photoelectric effect was still seen to happen even at low intensity. The classical description of light as a wave started to wane, allowing the young fresh faced quantum theories to take shape. Quantum mechanics describes light as consisting of photons which carry quantised amounts of energy. Basically you split the light wave into neat little balls, with the size of the ball proportional to the frequency. If the ball size matches the transition energy needed for the electron to ping off, ionisation is seen to occur. Tuning the intensity only changes the number of photons being released, however, tuning the frequency changes the ball size which will either provide a better or worse ‘fit’ that affects the ionisation rate.

Brillouin scattering occurs when light travelling in a medium interacts with time independent (fluctuating) optical density variations caused by fancy things like phonons, magnons or the less impressive sounding temperature gradient. It is seen as a quantum mechanical treatment of photons interacting with quasi-particles like the magnon (acoustic modes of the material) but is intrinsictly differentfrom certain types of Rayleigh scattering (which involves random incoherent thermal fluctuations wheras Brillouin is a correlated periodic fluctuation) and Raman scattering (where the photons are scattered by an interaction with the vibrational and rotational transitions which are non propagating whereas Brillouin scattering involves propagating low frequency modes)